no code implementations • 15 Apr 2020 • Nima Anari, Kuikui Liu, Shayan Oveis Gharan, Cynthia Vinzant
For a matroid of rank $k$ on a ground set of $n$ elements, or more generally distributions associated with log-concave polynomials of homogeneous degree $k$ on $n$ variables, we show that the down-up random walk, started from an arbitrary point in the support, mixes in time $O(k\log k)$.
Data Structures and Algorithms Discrete Mathematics Probability
no code implementations • 2 Jul 2018 • Nima Anari, Shayan Oveis Gharan, Cynthia Vinzant
We give a deterministic polynomial time $2^{O(r)}$-approximation algorithm for the number of bases of a given matroid of rank $r$ and the number of common bases of any two matroids of rank $r$.
Data Structures and Algorithms Information Theory Combinatorics Information Theory Probability
